Numerical Performance Analysis of Soliton in Higher Nonlinear Medium Influenced by Quantum Potential

An optical soliton, also known as a soliton pulse, is a special kind of wavepacket that travels through a nonlinear medium with a constant speed, undistorted profile, and conserved energy and momentum. The nonlinear Schrödinger equation (NLSE) precisely balances the nonlinear and dispersion factors to produce this steady propagation. In this work, extensive numerical analysis is carried out to the NLSE with quadratic-cubic nonlinearity to describe the characteristics of optical soliton propagation. Specifically, we considered a perturbation term, quantum potential or the Bohm potential, to investigate the influence of perturbations on the propagation of optical solitons. The stability of the solitary pulse propagation by varying the strength of quantum potential, quadratic and cubic nonlinearities are well studied. To do so, we built a mathematical model of NLSE with quadratic-cubic nonlinearity and quantum potential and obtained the numerical solutions through the finite element method. We observed the stability and amplitude of the optical soliton pulse over a specific time interval for different values of the parameters. We investigated the suitable choice of parameters for stable pulse propagation. We found that optical soliton pulse propagation was stable when self-focusing nonlinearity equaled self-defocusing nonlinearity at a medium strength of quantum potential perturbation. In particular, for the Bohm potential, b= 0.4, and quadratic and cubic nonlinearity coefficients of
$c$

1
= 0.3, and
$c$

2
=-0.3, stable soliton transmission was demonstrated which has less distortion and minimum amplitude variation. This model is important for studying the dynamics of solitons, perturbations in the transmission system, and optimizing the transmission system for stable soliton transmission.